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A068140 Smaller of two consecutive numbers each divisible by a cube. 14
80, 135, 296, 343, 351, 375, 512, 567, 624, 728, 783, 944, 999, 1160, 1215, 1375, 1376, 1431, 1592, 1624, 1647, 1808, 1863, 2024, 2079, 2240, 2295, 2375, 2400, 2456, 2511, 2624, 2672, 2727, 2888, 2943, 3087, 3104, 3159, 3320, 3375, 3429, 3536, 3591 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Cubeful numbers with cubeful successors. This is to cubes as A068781 is to squares. 1375 is the smallest of three consecutive numbers divisible by a cube, since 1375 = 5^3 * 11 and 1376 = 2^5 * 43 and 1377 = 3^4 * 17. What is the smallest of four consecutive numbers divisible by a cube? Of n consecutive numbers divisible by a cube? - Jonathan Vos Post, Sep 18 2007

22624 is the smallest of four consecutive numbers each divisible by a cube, with factorizations 2^5 * 7 * 101, 5^3 * 181, 2 * 3^3 * 419, and 11^3 * 17.  [D. S. McNeil, Dec 10 2010]

18035622 is the smallest of five consecutive numbers each divisible by a cube. 4379776620 is the smallest of six consecutive numbers each divisible by a cube. 1204244328624 is the smallest of seven consecutive numbers each divisible by a cube. [Donovan Johnson, Dec 13 2010]

The sequence is the union, over all pairs of distinct primes (p,q), of numbers == 0 mod p^3 and == -1 mod q^3 or vice versa. - Robert Israel, Aug 13 2018

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

{k such that k is in A046099 and k+1 is in A046099}. - Jonathan Vos Post, Sep 18 2007

EXAMPLE

343 is a term as 343 = 7^3 and 344= 2^3 * 43.

MAPLE

isA068140 := proc(n)

    isA046099(n) and isA046099(n+1) ;

end proc:

for n from 1 to 4000 do

    if isA068140(n) then

        printf("%d, ", n) ;

    end if;

end do: # R. J. Mathar, Dec 08 2015

MATHEMATICA

a = b = 0; Do[b = Max[ Transpose[ FactorInteger[n]] [[2]]]; If[a > 2 && b > 2, Print[n - 1]]; a = b, {n, 2, 5000}]

Select[Range[2, 6000], Max[Transpose[FactorInteger[ # ]][[2]]] > 2 && Max[Transpose[FactorInteger[ # + 1]][[2]]] > 2 &] (* Jonathan Vos Post, Sep 18 2007 *)

CROSSREFS

Cf. A046099, A063528, A068781, A068782, A068783, A068784, A122692, A174113.

Sequence in context: A062376 A223087 A261549 * A224547 A204648 A202447

Adjacent sequences:  A068137 A068138 A068139 * A068141 A068142 A068143

KEYWORD

easy,nonn

AUTHOR

Amarnath Murthy, Feb 22 2002

EXTENSIONS

Edited and extended by Robert G. Wilson v, Mar 02 2002

Title edited, cross-references added by Matthew Vandermast, Dec 09 2010

STATUS

approved

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Last modified December 15 09:05 EST 2019. Contains 329995 sequences. (Running on oeis4.)